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Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…
Dimensionality reduction (DR) methods are commonly used for analyzing and visualizing multidimensional data. However, when data is a live streaming feed, conventional DR methods cannot be directly used because of their computational…
This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the $d$-dimensional integral of a given function. The new algorithm, called the MDI-SG ({\em multilevel…
We develop deep Poisson-gamma dynamical systems (DPGDS) to model sequentially observed multivariate count data, improving previously proposed models by not only mining deep hierarchical latent structure from the data, but also capturing…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…
We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories…
With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…
We have recently seen great progress in 3D scene reconstruction through explicit point-based 3D Gaussian Splatting (3DGS), notable for its high quality and fast rendering speed. However, reconstructing dynamic scenes such as complex human…
Dimensionality reduction techniques are widely used for visualizing high-dimensional data in two dimensions. Existing methods are typically designed to preserve either local (e.g., $t$-SNE, UMAP) or global (e.g., MDS, PCA) structure of the…
Multimodal synthetic data generation is crucial in domains such as autonomous driving, robotics, augmented/virtual reality, and retail. We propose a novel approach, GenMM, for jointly editing RGB videos and LiDAR scans by inserting…
Detecting objects in 3D LiDAR data is a core technology for autonomous driving and other robotics applications. Although LiDAR data is acquired over time, most of the 3D object detection algorithms propose object bounding boxes…
This article presents an empirical validation of the functional multidimensional scaling model, a novel approach that improves the smoothness of time-varying dissimilarities in a low-dimensional space, embedding a modified Adam stochastic…
Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…
Traditional methods for solving linear systems have quickly become impractical due to an increase in the size of available data. Utilizing massive amounts of data is further complicated when the data is incomplete or has missing entries. In…
The recent proliferation of 3D content that can be consumed on hand-held devices necessitates efficient tools for transmitting large geometric data, e.g., 3D meshes, over the Internet. Detailed high-resolution assets can pose a challenge to…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
While deep generative models (DGMs) have gained popularity, their susceptibility to biases and other inefficiencies that lead to undesirable outcomes remains an issue. With their growing complexity, there is a critical need for early…
3D Gaussian Splatting SLAM has emerged as a widely used technique for high-fidelity mapping in spatial intelligence. However, existing methods often rely on a single representation scheme, which limits their performance in large-scale…
Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models,…